Abstract

It is shown that the guided-mode resonance effects associated with waveguide gratings can be used to realize transmission bandpass filters. The key idea is the integration of the resonant waveguide gratings into a dielectric multilayer structure that efficiently reflects the off-resonance spectral components while passing the resonant part. This concept is applied to design multilayer transmission bandpass filters with high efficiency, narrow linewidth, symmetrical response, and low sidebands.

© 1995 Optical Society of America

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References

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  1. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.
  2. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
    [Crossref]
  3. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
    [Crossref] [PubMed]
  4. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [Crossref]
  5. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
    [Crossref] [PubMed]
  6. R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
    [Crossref]
  7. A. Hessel, A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
    [Crossref]
  8. L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
    [Crossref]
  9. H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
    [Crossref]
  10. M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).
  11. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [Crossref] [PubMed]
  12. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [Crossref]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

1995 (1)

1994 (2)

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[Crossref] [PubMed]

1993 (1)

1992 (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

1990 (1)

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

1989 (1)

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
[Crossref]

1985 (2)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[Crossref]

1965 (1)

A. Hessel, A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[Crossref]

Bagby, J. S.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Bertoni, H.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
[Crossref]

Black, T. D.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Cheo, L.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
[Crossref]

Gale, M. T.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Hessel, A.

A. Hessel, A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[Crossref]

Knop, K.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Magnusson, R.

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[Crossref] [PubMed]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[Crossref] [PubMed]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[Crossref] [PubMed]

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Mashev, L.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[Crossref]

Moharam, M. G.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Morf, R. H.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Oliner, A. A.

A. Hessel, A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[Crossref]

Popov, E.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[Crossref]

Sohn, A.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

Tamir, T.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
[Crossref]

Wang, S. S.

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[Crossref] [PubMed]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[Crossref] [PubMed]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[Crossref] [PubMed]

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[Crossref]

IEEE Trans. Antennas Propagat. (2)

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antennas Propagat. 42, 567–569 (1994).
[Crossref]

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propagat. 37, 78–83 (1989).
[Crossref]

J. Opt. Soc. Am. A (1)

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
[Crossref]

Opt. Commun. (1)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

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Figures (8)

Fig. 1
Fig. 1

Multilayer, square-wave profile waveguide grating model. The zero-order backward-diffracted wave (R) and the corresponding forward-diffracted wave (T) are propagating waves with all higher-order diffracted waves being cut off at normal incidence.

Fig. 2
Fig. 2

Resonance wavelength (λ/Λ) location as a function of normalized thickness (t/Λ) for a double-layer waveguide grating structure. Line a represents a quarter-wave design (t = λ) with line b yielding a half-wave design (t = 2λ) because d 1 = t/4(∊1,eff)1/2 and d 2 = t/4(∊2)1/2. The parameters are ∊ c = 1.0, ∊1,eff = 5.52, ∊2 = 1.9, ∊ s = 2.31, and Λ = 1.0 μm, at normal incidence (θ′ = 0°).

Fig. 3
Fig. 3

TE spectral response of a double-layer waveguide-grating filter at normal incidence. The parameters are ∊ c = 1.0, ∊1H = 5.86, ∊1L = 5.2, ∊2 = 1.9, ∊ s = 2.31, Λ = 1.0 μm, θ′ = 0°, and thicknesses d 1 = 0.404 μm and d 2 = 0.688 μm (half-wave thicknesses at resonance).

Fig. 4
Fig. 4

TE spectral response of a double-layer waveguide-grating filter at normal incidence. The parameters are ∊ c = 1.0, ∊1H = 5.86, ∊1L = 5.2, ∊2 = 1.9, ∊ s = 2.31, Λ = 1.0 μm, θ′ = 0°, and thicknesses d 1 = 0.170 μm and d 2 = 0.290 μm (quarter-wave thicknesses).

Fig. 5
Fig. 5

TE spectral response of a two-HL-layer-pair waveguide-grating transmission filter with layers 1 and 3 being modulated. The parameters are ∊ c = 1.0, ∊ s = 2.31, ∊1H = ∊3H = 6.25, ∊1L = ∊3L = 4.84, ∊2 = 1.9, Λ = 0.3 μm, θ′ = 0°, d 1 = d 3 = 0.05 μm, and d 2 = d 4 = 0.087 μm (quarter-wave thickness near resonance).

Fig. 6
Fig. 6

TE spectral response of a four-HL-layer-pair waveguide-grating filter with layers 1 and 7 being modulated. The parameters are ∊ c = 1.0, ∊ s = 2.31, ∊1H = ∊7H = 6.25, ∊1L = ∊7L = 4.84, ∊3 = ∊5 = 5.52, ∊2 = ∊4 = ∊6 = 1.9, θ′ = 0°, and Λ = 0.3 μm; grating thicknesses are 0.051 μm for odd-numbered layers and 0.087 μm for even-numbered layers.

Fig. 7
Fig. 7

TE spectral response of a nine-layer transmission filter with the top layer and the bottom layer being waveguide gratings. The parameters are ∊ c = 1.0, ∊ s = 2.31, ∊1H = ∊9H = 6.25, ∊1L = ∊9L = 4.84, ∊3 = ∊5 = ∊7 = 5.52, ∊2 = ∊4 = ∊6 = ∊8 = 1.9, Λ = 0.3 μm, and θ′ = 0°; grating thicknesses are 0.051 μm for odd-numbered layers and 0.087 μm for even-numbered layers.

Fig. 8
Fig. 8

TE spectral response of an 11-layer transmission filter with layers 1 and 11 being waveguide gratings. The parameters are the same as those in Fig. 7 except that one additional HLpair is inserted between the top grating and the bottom grating.

Equations (1)

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R = [ 1 ( s c ) 1 / 2 ( 1 , eff 2 , eff ) N ] 2 [ 1 + ( s c ) 1 / 2 ( 1 , eff 2 , eff ) N ] 2 ,

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